Solve Equations using a Matrix

[2slowtogofast]

solve equations using a matrix

x + y -z = 0
3x - y + z = 4
5x +z = 7

so i wrote the matrix

1 1 -1 0
3 -1 1 4
5 0 1 7

then i multiplied Row 1 by -3 and added that to row 2
and multiplied row 1 by -5 and added that to row 3
resulting in

1 1 -1 0
0 -4 4 4
0 -5 6 7

then i multiplied row 2 by - 1/4

1 1 -1 0
0 1 -1 -1
0 -5 6 7

then multiplied row 2 by 5 and added that to row 3

1 1 -1 0
0 1 -1 -1
0 0 1 2

now i subbed back into eqns

x + y -z = 0
3x - y + z = 4
5x +z = 7

1x + 1y - 1z = 0
0x +1y - 1z = -1
0x + 0y + 1z = 2

so z = 2 and solving all the other equation i get x = 1 and y = 1
is this right because i tried solving these by subtraction and got somthing different

 

[neu]

You have not constructed a matrix equation, you have just rewritten the coefficients in some kind of array/pattern

THe matrix equation is :

$$\begin{pmatrix}<br /> 1 & 1 & -1\\<br /> 3&-1 & 1\\<br /> 5&0&1<br /> \end{pmatrix}<br /> \begin{pmatrix}<br /> x\\<br /> y\\<br /> z<br /> \end{pmatrix}<br /> =<br /> \begin{pmatrix}<br /> 0\\<br /> 4\\<br /> 7<br /> \end{pmatrix}<br />$$

 

[happyg1]

The augmented matrix that 2slow to go fast used is correct.
All you need to do is plug x y and z back into your original equations and see if they make true statements.
Looks to me like they check out.
CC

 

[montoyas7940]

It looks good to me.

https://www.physicsforums.com/misc/howtolatex.pdf


$$\begin{pmatrix}<br /> x\\<br /> y\\<br /> z<br /> \end{pmatrix}<br /> =<br /> \begin{pmatrix}<br /> 1\\<br /> 1\\<br /> 2<br /> \end{pmatrix}<br />$$

 

[2slowtogofast]

i just got it i was substituting wrong thanks for the help